An exemplary prior art cable with a tensionproof cable jacket is disclosed in published German patent application DE-OS 34 14 638. It contains a tensionproof open-mesh tape which consists of longitudinal aramid threads and cross threads of another plastic, and over which an outer plastic covering is extruded. When the latter shrinks, the tensionproof tape becomes wavy, so that subsequently applied tensile forces will not be absorbed by the tape until the latter has been completely straightened.